Key words: decimal unit, maximum number unit is 1/2, number of decimal units, maximum number unit is 0.5, number of decimal units, semi-integer property, why 1+ 1=2, etc.
1, preface:
Why 1+ 1=2? In order to answer such a mathematical contradiction, elementary mathematics needs to introduce new concepts and definitions, such as decimal units, the largest decimal unit is 0.5, the number of decimal units, semi-integer properties and so on.
Such a new mathematical concept, definition and connotation are simple and profound. If we don't introduce some new mathematical concepts, dialectical understanding and dialectical understanding, we can't understand and accept mathematical theory in any case.
Why 1+ 1=2 is the key, difficult and resistance point of the mathematical contradiction why 1+ 1=2. At the same time, it is clearly pointed out why 1+ 1=2 is definitely not an arithmetic axiom 1+ 1.
It is the basic principle and philosophy contained in the scientific answer arithmetic axiom 1+ 1=2. It is hoped that mathematicians and math teachers will take the lead in changing the traditional mathematical thinking concept and facing up to the mathematical truth.
2. Review the concept of score:
1?o'clock
Anyone with mathematical knowledge knows the score, the number of copies (the number of fractional units), the fractional unit, …, what is a score and what is a fractional unit? How many copies are there? What is a decimal counting unit? Let's review the scores.
Concept, divide a unit "1" into several equal parts, and the number representing such one or several parts is called a fraction, such as 1/2, 1/5, 2/6, 7/3. The general form of the fraction is m/n (both m and n are positive integers.
Number), …, n is the number of copies into which a unit "1" is divided, which is called the denominator of this fraction, 1/n is the number representing one of them, which is called the fractional unit, and m represents its number of copies, which is m fractional units.
The horizontal line (diagonal line in this paper) in the middle of the "numerator" called this fraction is called "fractional line", and the denominator n stipulates that it cannot be zero, …, when the above m is negative, m/n is negative, and the positive and negative fractions are collectively called points.
Count.
The decimal unit is 1/n, when n= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... then 1/2, 1/3.
/10, ... is the unit of fraction, ..., while when n= 1/n =1=1is a special case, which belongs to integer fraction and should be another matter. Obviously, the maximum value is different.
Edit paragraph 3 to review the concept of decimal counting unit:
small
Number counting unit refers to the most representative decimal unit in decimal counting method, which is 0.1(110) and 0.0 1( 1) respectively.
/100), 0.001(11000), ..., the maximum decimal counting unit is 0. 1, which is not enough for rational understanding in elementary mathematics, because decimal lists.
The concept of bit covers the meaning and significance of decimal counting unit, and the largest decimal counting unit is 0. 1, not 0.5. The concept of decimal counting unit has a deeper and broader meaning, covering decimal counting unit and decimal.
The absolute value of is only part of the decimal connotation. Therefore, if some new concepts are not introduced, such as decimal unit, the number of decimal units, the maximum decimal unit is 0.5, and the semi-integer property, it is impossible to return correctly.
Answer the mathematical truth: Why 1+ 1=2? Ask the math teacher to think about it! …。
4, what is the decimal unit:
such as
If the decimal unit is 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8,/.
Formula: 0.5, 0.3 (), 0.25, 0.2, 0. 16 (), 0. 142857 (), 0. 125, 0. 1 (), 0.
0.5, 0.3 (), 0.25, 0.2, 0. 16 (), 0. 142857 (), 0. 125, 0. 1 (), 0. 1.
In order to divide decimals into 0.5, 0.3 (), 0.25, 0.2, 0. 16 (), 0. 142857 (), 0. 125, 0. 1 (), 0.
This is an extremely important and indispensable understanding. Fractions correspond to decimals, decimal units correspond to decimal units, decimal units correspond to decimal units, and decimal units correspond to decimal units.
Is a relatively whole, ...
5, the maximum number of units is 0.5:
because
If 1/2 is the largest decimal unit, then 0.5 is the largest decimal unit, and decimal units and decimal units correspond to each other and are equivalent to each other. Therefore, primary school mathematics textbooks all agree that 1/2 is the largest score list.
Bit, then elementary mathematics textbooks also need and must realize that 0.5 is the largest decimal unit, fractions and decimals correspond to each other, and the number of copies (the number of decimal units) corresponds to the number of decimal units, which is the largest decimal list.
1/2 bits correspond to the largest decimal unit of 0.5, so besides irrational numbers, we should look at the problem in connection with each other. Therefore, it is correct and appropriate to introduce decimal unit, and the largest decimal unit is 0.5, which is a semi-integer property.
Practical! We need people to change their concepts of mathematical thinking, understand and treat them correctly dialectically.
6. What are the semi-integral properties?
one half
Integer property: the absolute values of other decimals are compared with semi-integers.
0.5, -0.5, 1.5, - 1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -4.5, -5.5, -6.5, ...
Values are more fragmented, in other words, semi-integers.
0.5, -0.5, 1.5, - 1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -4.5, -5.5, -6.5, ...
Compared with other decimals, the absolute value of the value is relatively complete. In the axiomatic system of numerical logic, the relatively complete properties obtained by this comparison are collectively called semi-integers.
Half integers of 0.5, -0.5, 1.5,-1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -5.5, -6.5, ...
Attribute, why is it a half integer?
0.5, -0.5, 1.5, - 1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -4.5, -5.5, -6.5, ...
Values will have the property of semi-integer, because their decimal unit is the largest decimal unit of 0.5, which determines the semi-integer.
0.5, -0.5, 1.5, - 1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -4.5, -5.5, -6.5, ...
Value has the property of semi-integer, so it is only semi-integer.
0.5, -0.5, 1.5, - 1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -4.5, -5.5, -6.5, ...
Values have the property of semi-integer, and can be determined all at once without verification one by one. This is a rule, other decimals do not have the nature of semi-integer, because the decimal units of other decimals.
0.3 (), 0.25, 0.2, 0. 16 (), 0. 142857 (), 0. 125, 0. 1 (), 0. 1, ...
0.5, which can be completely excluded at one time, does not need to be verified one by one. This is also a law. The semi-integral nature of semi-integers is the "winding" of arithmetic axioms, which needs dialectical analysis and dialectical understanding by dialectical logic, and needs to be treated correctly and emphasized again.
Explain, don't get me wrong, not all decimals have the property of semi-integer, let alone the greater the absolute value of decimals, they only have the property of semi-integer.
0.5, -0.5, 1.5, - 1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -4.5, -5.5, -6.5, ...
Value has the property of semi-integer, otherwise it is a misreading and misunderstanding of the semi-integer property (relative integral property).
7. Why 1+ 1=2:
Even numbers can be naturally divisible by 2 in the abstract, odd numbers can't be naturally divisible by 2 in the abstract, and odd numbers (including prime numbers) can be divisible by 2 and a half in the abstract, because the fractional form of semi-integer is 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5. 1+ 1=2 or 2 is the primary axiom of mathematics, and the Goldbach conjecture of number theory-"1+1"is that the arithmetic axiom of even links in the axiom system of numerical logic exists objectively, which neither affirms nor denies ambiguity and does not conform to law of excluded middle; Its philosophical significance (philosophy): even numbers can be naturally divisible by 2 in the abstract sense, odd numbers cannot be naturally divisible by 2 in the abstract sense, and odd numbers (including prime numbers) can actually be divisible by 2 and a half in the abstract sense. Traditionally, even numbers can be divisible by 2, and odd numbers cannot be divisible by 2, which means the exclusion, opposition and difference between odd numbers and even numbers. Even numbers are divisible by 2, odd numbers are divisible by 2, and odd numbers are divisible by 2. In the abstract sense, it means that there are similarities in differences between odd numbers and even numbers, and there are similarities in differences, which coincides with the law of unity of opposites in philosophy. Therefore, odd numbers and even numbers (semi-integers in the form of integers and fractions or semi-integers in the form of integers and fractions, and semi-integers in the form of integers and semi-integers) are opposites, unified and complementary. 1+ 1=2 contains the profound law of unity of opposites in numerical logic. In other words, odd and even numbers (integers and semi-integers) contain the law of unity of opposites in philosophy, which is the basic principle and philosophy contained in the arithmetic axiom 1+ 1=2. Philosophy (dialectics of nature) starts from the law of unity of opposites and injects pure mathematics and elementary education. Why 1+ 1=2 does not question the correctness of the arithmetic (mathematics) axiom 1+ 1=2, but scientifically answers the basic principles and philosophies contained in the arithmetic (mathematics) axiom 1+ 1=2; applied mathematics
The objective law of 1+ 1=2 has been tested and proved by countless human practices, and it has long been proved to be the correct truth of natural science, and the theory of pure mathematics (mathematical basis) is still being explored.
It is the basic status quo of pure mathematics (mathematical foundation), ...; As the saying goes, the simplest, simplest and most profound, mathematics has been fulfilled. Why 1+ 1=2, the simplest numerical logic, contains the deepest?
Carve truth, the law of unity of opposites, generalized integers and generalized mathematical truth. Integers in mathematics have a generalized unit of scientific abstraction "1", and fractional semi-integers have a generalized scientific abstraction.
The largest decimal unit "1/2" and semi-integer (semi-integer) have the largest decimal unit "0.5" in the generalized scientific abstraction, which is the most abstract mathematical meaning of mathematics (arithmetic).
Sequence, concept, definition, fraction is fraction, fractional nature, decimal is decimal, fractional nature However, the semi-integer nature of a semi-integer appeared, testing the courage and wisdom of human science! …。
8, generalized integer:
Integer and semi-integer are collectively referred to as generalized integers. Therefore, number theory breaks through traditional number theory, set theory breaks through traditional set theory and forms generalized number theory, and set theory forms generalized set theory. People need to change the traditional mathematical thinking concept! Those with different views, seek common ground while reserving differences!
9. Odd numbers are divisible by 2. 5:
idol
Numbers are divisible by 2, and odd numbers are not divisible by 2. In quantum mechanics, semi-integer has the property of semi-integer, which is innate.
Numbers) 0.5, -0.5, 1.5,-1.5, 2.5, -2.5, 3.5, -3.5, 4.5, -4.5, 5.5, -5.5. . . . . . Odd numbers are divisible by 2. 5.
To provide scientific and objective theoretical basis and support, 2 is the first axiom of mathematics, which completely breaks through the serious shackles of traditional mathematical concepts ... Author:,,, Address: Gu, Hekou District, Dongying City, Shandong Province
Island Oil Production Plant Area 3 Zip code: 257200 References: [1], original author: (American mathematician) M. Klein's Thoughts on Ancient and Modern Mathematics (translated by the Translation Group of Mathematics History of Peking University Mathematics Department) Shanghai Branch.
Published by Science and Technology Press, 198 1 July, [M]. [2], editor: Gu Chaohao, Mathematical Dictionary: Shanghai Dictionary Publishing House, 1993 1 1 month, [M].
References:
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